Question

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from the second day to the ninth day becomes 66. The number of copies sold on the first day of the book launch is:

Hint:

When dealing with averages over overlapping time intervals, convert each average to a total sum. Then, use differences of these sums to find individual day values and set up equations to solve for the unknowns.

Answer 1

Correct Answer: 59

Step 1: The average of days 1 to 8 is \(63\), so the total for those 8 days \(=504\); since the total for the first 7 days is \(420\), day 8's sales \(= 504-420=84\), and day 9's sales \(=84-11=73\).
Step 2: Moving the 8-day window from "days 1-8" to "days 2-9" drops \(d_1\) and adds \(d_9\). The average shifts from \(63\) to \(66\), a rise of \(3\) per day over \(8\) days, so \(d_9 - d_1 = 3\times8=24\).
Step 3: Since \(d_9=73\), \(d_1 = 73-24\).
\[ \boxed{d_1 = 49} \]